Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 74-89

BAYES ESTIMATION OF DIRICHLET PROCESS PARAMETER

By

JOSE G. LEITE, University of S\=ao Paulo, S\=ao Paulo
VICTOR H. SALINAS-TORRES,University of Santiago, Santiago
RAM C. TIWARI,University of North Carolina, Charlotte
and
JYOTI N. ZALKIKAR ,Florida International University, Miami

SUMMARY. Dirichlet process serves as a prior for the unknown distribution function in nonparametric Bayes estimation of various parameters. The present article addresses the problem of finding Bayes estimator of Dirichlet process parameter itself, with respect to the discrete prior distribution concentrating on finite number of fixed points. This problem is related to the estimation of the parameter of independent and non-identically distributed Bernoulli model. We show that in the limiting case as the sample size increases to infinity, the Bayes estimator converges to the prior supported point ``closest'' to the ``true'' parameter value, which may not be a prior-supported point. This result exemplifies a typical Bayesian phenomenon that the posterior distribution is dominated by the prior distribution.

AMS (1991) subject classification. Primary 62G05; secondary 62C10, 60G99.

Key words and phrases. Jensen's inequality, prior sample size, maximum likelihood estimator.

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